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International Theoretical Science Journal
Volume 59 >>> № 3 MAY — JUNE 2023
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UDC 517.988
V.V. Semenov1, S.V. Denisov2


1 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

 semenov.volodya@gmail.com

2 Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

 sireukr@gmail.com

IMPULSE TRAJECTORY AND FINAL CONTROLLABILITY
OF PARABOLIC-HYPERBOLIC SYSTEMS

Abstract. The authors investigate the existence and uniqueness of generalized solutions of boundary-value problems for equations of the parabolic-hyperbolic type with generalized functions of finite order on the right-hand sides. The motivation is the analysis of the problems of trajectory and final controllability of systems described by these boundary-value problems and subjected to concentrated influences of the impulse or point type. The systems can be considered «toy models» of the interaction of a solid body and a liquid. A priori inequalities in negative norms are obtained. The theorems of existence and uniqueness of generalized solutions and theorems of trajectory and final controllability of systems with singular influences are proved.

Keywords: controllability, equations of parabolic-hyperbolic type, a priori inequalities, negative norms, generalized solution, impulse control.


full text

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